A real number $x$ satisfies $x-1/x=6$. Then $x^2+1/x^2$ equals:

Squaring the given relation, $(x-1/x{)}^2=x^2-2+1/x^2=36$, so $x^2+1/x^2=36+2=38$. (34 subtracts the 2 — that would be the answer if the given expression were $x+1/x$; 36 forgets the middle term altogether; 40 adds 4 instead of 2.) Numerically $x=3$ + √10 ≈ 6.1623, so $x^2$ ≈ 37.974 and $1/x^2$ ≈ 0.026, adding to 38.